Nonlinear energy amplification of turbulent flows over progressive surface waves

We proposed a novel reduced-order model that extends resolvent formulation from flat walls to waving walls with a curvilinear grid for problems such as wind-wave interaction. Large-eddy simulations with various wave ages are performed to obtain the two-dimensional time-averaged flows. Utilizing Floquet theory with a curvilinear boundary-fitted grid, the nonlinear effects induced by the wave are described accurately. We investigate the mechanisms of nonlinear energy amplification for different wave ages and the associated energy transfer among different scales. The results enhance our understanding of the wave effects on resolvent modes and the corresponding energy transfer mechanism (triadic interaction) from an input/output perspective.